Simple Uniaxial Extension Research Articles

Harnessing shape optimization techniques to develop novel methods to determine shear properties in PMCs

Shape optimization techniques are utilized to develop an optimal shear specimen for polymer matrix composites (PMCs) in which shear stresses result from simple uniaxial extension. An expanding array of composite applications means certification and damage tolerance are critical design factors. This methodology improves the ease of characterization for classically challenging material properties, such as shear failure. Numerical simulations were conducted using IM7/977-3 unidirectional prepreg mechanical properties. Large shear strain concentrations in the region of interest led to predicted failure in the region of interest under conditions consistent with shear. The geometry generated by the shape optimization should continue to be explored due to its capability generating a geometry which can measure the shear modulus and shear strength of a laminate. The shape optimization method’s ability to tailor a sample geometry for a desired strain state and failure mode leads the authors to recommend exploration of additional optimized test geometries for other failure modes and materials, in addition to the experimental investigation of the geometry generated for shear.

On biological availability dependent bone remodeling

Modeling the evolution of bone density is relevant for understanding, simulation and possible prediction of bone response to external and internal influences. In this work we present a formulation for the bone density evolution process that takes into account not only the commonly considered mechanical stimulus, but, as novelty, also the influence of the availability of nutrients and hormones, with its implementation pursued within the finite element method. A simple uni-axial extension test is used to illustrate and compare our novel model against the classical approach. The results of the proposed modified model are promising for application to real-life problems.

On age-dependent bone remodeling

A number of previous studies have investigated the possibilities of modelling the change in density of bones. Remodeling can be formulated at the constitutive or the kinematic level. In this work we introduce a formulation for the density growth process which takes not only the mechanical stimulus into account but also the influence of age on the evolution of growth. We demonstrate the implementation in the context of the finite element method. This novel approach is illustrated for a simple uniaxial extension test and is verified against previous numerical results. Moreover, two further physiologically motivated examples are performed. The results of the proposed modified model show excellent agreement with comparable results from literature and are promising for the application to real-life problems.

High-Weissenberg predictions for micellar fluids in contraction–expansion flows

This study is concerned with the numerical modelling of thixotropic and non-thixotropic materials in contraction–expansion flows at high Weissenberg number (We). Thixotropy is represented via a new micellar time-dependent constitutive model for worm-like micellar systems and contrasted against network-based time-independent PTT forms. The work focuses on steady-state solutions in axisymmetric rounded-corner 4:1:4 contraction–expansion flows for the benchmark solvent-fraction of β=1/9 and moderate hardening characteristics (ε=0.25). In practice, this work has relevance to industrial and healthcare applications, such as enhanced oil-reservoir recovery and microfluidics. Simulations have been performed via a hybrid finite element/finite volume algorithm, based around an incremental pressure-correction time-stepping structure. To obtain high-We solutions, both micellar and PTT constitutive equation f-functionals have been amended by (i) adopting their absolute values appealing to physical arguments (ABS-correction); (ii) through a change of stress variable, Π=τp+(ηp0/λ1)I, that aims to prevent the loss of evolution in the underlying initial value problem; and finally, (iii) through an improved realisation of velocity gradient boundary conditions imposed at the centreline (VGR-correction). On the centreline, the eigenvalues of Π are identified with its Π-stress-components, and discontinuities in Π-components are located and associated with the f-functional-poles in simple uniaxial extension. Quality of solution is described through τrz, N1 and N2 (signature of vortex dynamics) stress fields, and Π-eigenvalues. With {micellar, EPTT} fluids, the critical Weissenberg number is shifted from critical states of Wecrit={4.9,220} without correction, to Wecrit={O(102),O(103)} with ABS–VGR-correction. Furthermore, such constitutive equation correction has been found to have general applicability.

Unified constitutive modeling of rubber-like materials under diverse loading conditions

This paper presents a new constitutive model that unifies the behavioral characterizations of rubber-like materials in a broad range of loading regimes. The proposed model combines a selection of existing components that are known to reflect, with suitable accuracy, two fundamental aspects of rubber behavior in finite strain: (i) rate-independent softening under deformation, also known as the Mullins effect, and (ii) hyper-viscoelasticity, including at high strain rates. The evolution model is further generalized to account for multiple rates of internal dissipation (or material time-scales). Suitable means of identifying the system’s parameters from simple uniaxial extension tests are explored. Several aspects of the model’s behavior are shown in virtual experiments of uniaxial extension, at different stretch rates. A possible directional approach extending the model to handle softening induced anisotropy is briefly discussed.

A theory of stress-softening in incompressible isotropic materials

A general theory of isotropic stress-softening in incompressible isotropic materials is developed. The principal idea is that a stress-softening material is an inelastic material that has selective memory of only the maximum previous deformation to which it is subjected. This memory dependence is incorporated within general material response functions that are monotone decreasing functions of a stress-softening variable, which is a monotone increasing function of the maximum previous strain experienced by the material. A loading criterion is introduced to identify when the material is loaded along its virgin deformation path where the maximum previous strain is its current value, and to identify when it is unloaded to deform subsequently as an ideal isotropic elastic material in both elastic loading and unloading, so long as the maximum previous strain is not exceeded. The effect of loading from a configuration of maximum previous strain is to further stress-soften the material. Results demonstrating the effects of stress-softening are obtained for general isotropic stress-softening materials in simple uniaxial extension and in simple shear. A simplified analytical model together with a special softening function are introduced to illustrate some general results and to provide specific analytical and graphical examples. Both general and model-specific analytical results obtained for simple uniaxial extension are shown to be consistent with the overall ideal phenomenological behavior exhibited in experiments by others on stress-softening in simple tension and compression. Similar but totally new results for simple shear are derived, and their relation to effects in simple tension are discussed. It is demonstrated that the larger effect of softening occurs in the simple uniaxial extension, the effect in even a gross equivalent simple shear being small. All results are obtained from general three-dimensional constitutive equations.

Poly(Dimethylsiloxane) Elastomers from Aqueous Emulsions: II. Mechanical Properties

Abstract Stress—strain measurements in simple uniaxial extension were used to characterize the mechanical properties of the elastomers prepared from poly(dimethylsilxoxane) emulsions as described in the preceding paper. The studies were carried out on the materials in the unswollen state, after they had received different treatments, specifically no aging, aging in the dry state, or aging in the wet (emulsion) state. Increase in silane crosslinker concentration was found to increase nominal stresses and moduli but to decrease extensibility, two changes that parallel the observed decreases in soluble polymer fractions and extents of equilibrium swelling reported earlier. The energy for rupture (“toughness”) frequently stays roughly constant because the decreased extensibility at least partially offsets the increased stresses. The changes in mechanical properties are due both to increased crosslinking and to reinforcing effects from silica generated from the silane, with the latter effect generally being the more important. The mechanical properties are much more affected by aging in the wet state, as opposed to aging in the dry state. For example, wet-aged elastomers generally had values of the nominal stress and modulus that were consistently lower than those for the unaged elastomers. Wet aging appears to be the result of the continual breaking and reforming of siloxane bonds in the aqueous environment of the emulsion, as probably accelerated by the presence of the tin catalyst.